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Concept: Inertial navigation system


Advances in the development of micro-electromechanical systems (MEMS) have made possible the fabrication of cheap and small dimension accelerometers and gyroscopes, which are being used in many applications where the global positioning system (GPS) and the inertial navigation system (INS) integration is carried out, i.e., identifying track defects, terrestrial and pedestrian navigation, unmanned aerial vehicles (UAVs), stabilization of many platforms, etc. Although these MEMS sensors are low-cost, they present different errors, which degrade the accuracy of the navigation systems in a short period of time. Therefore, a suitable modeling of these errors is necessary in order to minimize them and, consequently, improve the system performance. In this work, the most used techniques currently to analyze the stochastic errors that affect these sensors are shown and compared: we examine in detail the autocorrelation, the Allan variance (AV) and the power spectral density (PSD) techniques. Subsequently, an analysis and modeling of the inertial sensors, which combines autoregressive (AR) filters and wavelet de-noising, is also achieved. Since a low-cost INS (MEMS grade) presents error sources with short-term (high-frequency) and long-term (low-frequency) components, we introduce a method that compensates for these error terms by doing a complete analysis of Allan variance, wavelet de-nosing and the selection of the level of decomposition for a suitable combination between these techniques. Eventually, in order to assess the stochastic models obtained with these techniques, the Extended Kalman Filter (EKF) of a loosely-coupled GPS/INS integration strategy is augmented with different states. Results show a comparison between the proposed method and the traditional sensor error models under GPS signal blockages using real data collected in urban roadways.

Concepts: Accelerometer, Dead reckoning, Estimation theory, Unmanned aerial vehicle, Autocorrelation, Inertial navigation system, Signal processing, Global Positioning System


The integrated navigation system with strapdown inertial navigation system (SINS), Beidou (BD) receiver and Doppler velocity log (DVL) can be used in marine applications owing to the fact that the redundant and complementary information from different sensors can markedly improve the system accuracy. However, the existence of multisensor asynchrony will introduce errors into the system. In order to deal with the problem, conventionally the sampling interval is subdivided, which increases the computational complexity. In this paper, an innovative integrated navigation algorithm based on a Cubature Kalman filter (CKF) is proposed correspondingly. A nonlinear system model and observation model for the SINS/BD/DVL integrated system are established to more accurately describe the system. By taking multi-sensor asynchronization into account, a new sampling principle is proposed to make the best use of each sensor’s information. Further, CKF is introduced in this new algorithm to enable the improvement of the filtering accuracy. The performance of this new algorithm has been examined through numerical simulations. The results have shown that the positional error can be effectively reduced with the new integrated navigation algorithm. Compared with the traditional algorithm based on EKF, the accuracy of the SINS/BD/DVL integrated navigation system is improved, making the proposed nonlinear integrated navigation algorithm feasible and efficient.

Concepts: Better, Integral, Improve, Doppler effect, Inertial navigation system, Computational complexity theory, Dead reckoning, Signal processing


An actual account of the angle random walk (ARW) coefficients of gyros in the constant rate biased rate ring laser gyro (RLG) inertial navigation system (INS) is very important in practical engineering applications. However, no reported experimental work has dealt with the issue of characterizing the ARW of the constant rate biased RLG in the INS. To avoid the need for high cost precise calibration tables and complex measuring set-ups, the objective of this study is to present a cost-effective experimental approach to characterize the ARW of the gyros in the constant rate biased RLG INS. In the system, turntable dynamics and other external noises would inevitably contaminate the measured RLG data, leading to the question of isolation of such disturbances. A practical observation model of the gyros in the constant rate biased RLG INS was discussed, and an experimental method based on the fast orthogonal search (FOS) for the practical observation model to separate ARW error from the RLG measured data was proposed. Validity of the FOS-based method was checked by estimating the ARW coefficients of the mechanically dithered RLG under stationary and turntable rotation conditions. By utilizing the FOS-based method, the average ARW coefficient of the constant rate biased RLG in the postulate system is estimated. The experimental results show that the FOS-based method can achieve high denoising ability. This method estimate the ARW coefficients of the constant rate biased RLG in the postulate system accurately. The FOS-based method does not need precise calibration table with high cost and complex measuring set-up, and Statistical results of the tests will provide us references in engineering application of the constant rate biased RLG INS.

Concepts: Test method, Scientific method, Mathematics, Estimation, Gyroscope, Statistics, Ring laser gyroscope, Inertial navigation system


Inertial navigation systems use dead-reckoning to estimate the pedestrian’s position. There are two types of pedestrian dead-reckoning, the strapdown algorithm and the step-and-heading approach. Unlike the strapdown algorithm, which consists of the double integration of the three orthogonal accelerometer readings, the step-and-heading approach lacks the vertical displacement estimation. We propose the first step-and-heading approach based on unaided inertial data solving 3D positioning. We present a step detector for steps up and down and a novel vertical displacement estimator. Our navigation system uses the sensor introduced in the front pocket of the trousers, a likely location of a smartphone. The proposed algorithms are based on the opening angle of the leg or pitch angle. We analyzed our step detector and compared it with the state-of-the-art, as well as our already proposed step length estimator. Lastly, we assessed our vertical displacement estimator in a real-world scenario. We found that our algorithms outperform the literature step and heading algorithms and solve 3D positioning using unaided inertial data. Additionally, we found that with the pitch angle, five activities are distinguishable: standing, sitting, walking, walking up stairs and walking down stairs. This information complements the pedestrian location and is of interest for applications, such as elderly care.

Concepts: Proposal, Algorithm, Estimation theory, Strategic management, Estimator, Microelectromechanical systems, Automotive navigation system, Inertial navigation system


Wearable tracking devices incorporating accelerometers and gyroscopes are increasingly being used for activity analysis in sports. However, minimal research exists relating to their ability to classify common activities. The purpose of this study was to determine whether data obtained from a single wearable tracking device can be used to classify team sport-related activities. Seventy-six non-elite sporting participants were tested during a simulated team sport circuit (involving stationary, walking, jogging, running, changing direction, counter-movement jumping, jumping for distance and tackling activities) in a laboratory setting. A MinimaxX S4 wearable tracking device was worn below the neck, in-line and dorsal to the first to fifth thoracic vertebrae of the spine, with tri-axial accelerometer and gyroscope data collected at 100Hz. Multiple time domain, frequency domain and custom features were extracted from each sensor using 0.5, 1.0, and 1.5s movement capture durations. Features were further screened using a combination of ANOVA and Lasso methods. Relevant features were used to classify the eight activities performed using the Random Forest (RF), Support Vector Machine (SVM) and Logistic Model Tree (LMT) algorithms. The LMT (79-92% classification accuracy) outperformed RF (32-43%) and SVM algorithms (27-40%), obtaining strongest performance using the full model (accelerometer and gyroscope inputs). Processing time can be reduced through feature selection methods (range 1.5-30.2%), however a trade-off exists between classification accuracy and processing time. Movement capture duration also had little impact on classification accuracy or processing time. In sporting scenarios where wearable tracking devices are employed, it is both possible and feasible to accurately classify team sport-related activities.

Concepts: Thoracic vertebrae, Cervical vertebrae, Signal processing, Vertebral column, Microelectromechanical systems, Input device, Support vector machine, Inertial navigation system


The navigation accuracy of the inertial navigation system (INS) can be greatly improved when the inertial measurement unit (IMU) is effectively calibrated and compensated, such as gyro drifts and accelerometer biases. To reduce the requirement for turntable precision in the classical calibration method, a continuous dynamic self-calibration method based on a three-axis rotating frame for the hybrid inertial navigation system is presented. First, by selecting a suitable IMU frame, the error models of accelerometers and gyros are established. Then, by taking the navigation errors during rolling as the observations, the overall twenty-one error parameters of hybrid inertial navigation system (HINS) are identified based on the calculation of the intermediate parameter. The actual experiment verifies that the method can identify all error parameters of HINS and this method has equivalent accuracy to the classical calibration on a high-precision turntable. In addition, this method is rapid, simple and feasible.

Concepts: Gyroscope, Classical mechanics, Calibration, Scientific method, Metrology, Accelerometer, Measurement, Inertial navigation system


Digital tracking of human motion offers the potential to monitor a wide range of activities detecting normal versus abnormal performance of tasks. We examined the ability of a wearable, conformal sensor system, fabricated from stretchable electronics with contained accelerometers and gyroscopes, to specifically detect, monitor, and define motion signals and “signatures,” associated with tasks of daily living activities. The sensor system was affixed to the dominant hand of healthy volunteers (n = 4) who then completed four tasks. For all tasks examined, motion data could be captured, monitored continuously, uploaded to the digital cloud, and stored for further analysis. Acceleration and gyroscope data were collected in the x-, y-, and z-axes, yielding unique patterns of component motion signals for each task studied. Upon analysis, low-frequency (<10 Hz) tasks (walking, drinking from a mug, and opening a pill bottle) showed low intersubject variability (<0.3g difference) and low interrepetition variability (<0.1g difference) when comparing the acceleration of each axis for a single task. High-frequency (≥10 Hz) activity (brushing teeth) yielded low intersubject variability of peak frequencies in acceleration of each axis. Each motion task was readily distinguishable and identifiable (with ≥70% accuracy) by independent observers from motion signatures alone, without the need for direct visual observation. Stretchable electronic technologies offer the potential to provide wireless capture, tracking, and analysis of detailed directional components of motion for a wide range of individual activities and functional status.

Concepts: Inertial navigation system, Observation, Monitor lizard, Microelectromechanical systems, Gyroscope, Electronic engineering, Task, Activity


In order to meet the requirements of autonomy and reliability for the navigation system, combined with the method of measuring speed by using the spectral redshift information of the natural celestial bodies, a new scheme, consisting of Strapdown Inertial Navigation System (SINS)/Spectral Redshift (SRS)/Geomagnetic Navigation System (GNS), is designed for autonomous integrated navigation systems. The principle of this SINS/SRS/GNS autonomous integrated navigation system is explored, and the corresponding mathematical model is established. Furthermore, a robust adaptive central difference particle filtering algorithm is proposed for this autonomous integrated navigation system. The simulation experiments are conducted and the results show that the designed SINS/SRS/GNS autonomous integrated navigation system possesses good autonomy, strong robustness and high reliability, thus providing a new solution for autonomous navigation technology.

Concepts: Failure, Automotive navigation system, Mathematical model, Dead reckoning, Control theory, Autonomous robot, Inertial navigation system, Mathematics


To solve the navigation accuracy problems of multi-Unmanned Underwater Vehicles (multi-UUVs) in the polar region, a polar cooperative navigation algorithm for multi-UUVs considering communication delays is proposed in this paper. UUVs are important pieces of equipment in ocean engineering for marine development. For UUVs to complete missions, precise navigation is necessary. It is difficult for UUVs to establish true headings because of the rapid convergence of Earth meridians and the severe polar environment. Based on the polar grid navigation algorithm, UUV navigation in the polar region can be accomplished with the Strapdown Inertial Navigation System (SINS) in the grid frame. To save costs, a leader-follower type of system is introduced in this paper. The leader UUV helps the follower UUVs to achieve high navigation accuracy. Follower UUVs correct their own states based on the information sent by the leader UUV and the relative position measured by ultra-short baseline (USBL) acoustic positioning. The underwater acoustic communication delay is quantized by the model. In this paper, considering underwater acoustic communication delay, the conventional adaptive Kalman filter (AKF) is modified to adapt to polar cooperative navigation. The results demonstrate that the polar cooperative navigation algorithm for multi-UUVs that considers communication delays can effectively navigate the sailing of multi-UUVs in the polar region.

Concepts: Polar region, Earth, Rocket, Navigation, Kalman filter, Submarine, Inertial navigation system, Dead reckoning


Horizontal gravity disturbances are an important factor that affects the accuracy of inertial navigation systems in long-duration ship navigation. In this paper, from the perspective of the coordinate system and vector calculation, the effects of horizontal gravity disturbance on the initial alignment and navigation calculation are simultaneously analyzed. Horizontal gravity disturbances cause the navigation coordinate frame built in initial alignment to not be consistent with the navigation coordinate frame in which the navigation calculation is implemented. The mismatching of coordinate frame violates the vector calculation law, which will have an adverse effect on the precision of the inertial navigation system. To address this issue, two compensation methods suitable for two different navigation coordinate frames are proposed, one of the methods implements the compensation in velocity calculation, and the other does the compensation in attitude calculation. Finally, simulations and ship navigation experiments confirm the effectiveness of the proposed methods.

Concepts: Navigation, Automotive navigation system, Coordinate system, Dead reckoning, Effectiveness, Inertial navigation system, Effect, Frame of reference